Prescribed mean curvature hypersurfaces in conformal product manifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915895668899840 |
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| author | Gao, Qiang Zhou, Hengyu |
| author_facet | Gao, Qiang Zhou, Hengyu |
| contents | In this paper, we establish the existence of prescribed mean curvature (PMC) hypersurfaces in conformal product manifolds with (possibly empty) $C^{1,α}$ fixed graphical boundaries under a barrier condition. This result generalizes Gerhardt's work to non-flat conformal backgrounds. As a consequence, we obtain new solutions to the high-dimensional PMC Plateau problem with explicitly characterized topology. Moreover, under a quasi-decreasing condition on the PMC function, we demonstrate that the resulting hypersurfaces are $C^1$ graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Prescribed mean curvature hypersurfaces in conformal product manifolds Gao, Qiang Zhou, Hengyu Differential Geometry Analysis of PDEs 49Q20 In this paper, we establish the existence of prescribed mean curvature (PMC) hypersurfaces in conformal product manifolds with (possibly empty) $C^{1,α}$ fixed graphical boundaries under a barrier condition. This result generalizes Gerhardt's work to non-flat conformal backgrounds. As a consequence, we obtain new solutions to the high-dimensional PMC Plateau problem with explicitly characterized topology. Moreover, under a quasi-decreasing condition on the PMC function, we demonstrate that the resulting hypersurfaces are $C^1$ graphs. |
| title | Prescribed mean curvature hypersurfaces in conformal product manifolds |
| topic | Differential Geometry Analysis of PDEs 49Q20 |
| url | https://arxiv.org/abs/2401.14097 |